Answer the problem below

Question

The hands of a clock show 11:25. Express the obtuse angle formed by the hour and

minute hands in radian measure.

Answer 1

draw a clock diagram

angle is about pi,

slightly less than opposite sides of the clock

if the hour and minute hands formed a straight line the obtuse angle would be exactly pi radians

look at the right side of the clock from 12 to 5 is 5/12 of the circle =5/12 x 2pi= 25/60 x 2pi that's the minute hand

on the left side of the clock, the hour hand is between 11 and 12, about midway but not quite. it's 5/12 x 1/12 of the circle= 5/144 x 2pi from the hour hand to the top of the clock at 12

add those two angles together

(25/60 2pi) +(25/60 x 1/12 2pi)

=(5/12 +5/12x1/12) 2pi

=65/144 2pi

= 65/72 pi radians = slightly less than pi